where the sequence $\{a_{n}\}$ converges in some sense to $(c_{-}\mathbb{1}_{x<0}+c_{+}\mathbb{1}_{x>0})/x+\gamma \delta _{0}$. Here $\delta _{0}$ is the Dirac delta function concentrated at zero. A limit of $\{X_{n}\}$ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.